Towards optimal finite element error estimates for the penalized Dirichlet problem in a domain with curved boundary

We consider the finite element approximation of an elliptic problem with homogeneous Dirichlet boundary conditions on a curved boundary and imposed using the penalty method. We establish optimal H1 error estimates with suitable assumptions on the penalty parameter ε as a function of the elements size h. Our focus is on establishing these results with least restrictive assumptions possible on this dependency.